{"id":"W2022861720","doi":"10.1515/advgeom.2011.025","title":"On the symmetric average of a convex body","year":2011,"lang":"en","type":"article","venue":"Advances in Geometry","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Convex body; Combinatorics; Mixed volume; Regular polygon; Polytope; Asymmetry; Upper and lower bounds; Convex polytope; Volume (thermodynamics); Geometry; Mathematical analysis; Convex set; Convex hull; Physics; Convex optimization; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007518062,0.0001457466,0.0003056467,0.000813672,0.00004387578,0.000008162069,0.0003640053,0.00006371414,0.000666492],"category_scores_gemma":[0.003499635,0.00009507276,0.00007491471,0.002809376,0.0001004928,0.0002207312,0.00007426183,0.0002055077,0.00003390662],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002711092,"about_ca_system_score_gemma":0.00002143952,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002778821,"about_ca_topic_score_gemma":0.000006190311,"domain_scores_codex":[0.9987392,0.00005759668,0.0004204891,0.0001867997,0.0003205981,0.0002753064],"domain_scores_gemma":[0.996676,0.002595891,0.0002242321,0.0003877976,0.00008300535,0.00003302879],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003816591,0.0002230112,0.002109948,0.0002618717,0.00001856238,0.000007889235,0.0006105585,0.000005760455,0.00000854945,0.9929222,0.0001415585,0.003651851],"study_design_scores_gemma":[0.0003823432,0.0002720887,0.001636271,0.0001261376,0.00001352619,0.000005166823,0.0009133921,0.0000763745,0.005520529,0.9885215,0.00234078,0.0001918558],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7664788,0.004982085,0.006090082,0.000054822,0.0004082456,0.0003170231,0.00002577426,0.00005617015,0.221587],"genre_scores_gemma":[0.9971729,0.0006368725,0.001355091,0.0001716298,0.00002989126,0.00002337118,0.000001065937,0.00001552976,0.0005936786],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.230694,"threshold_uncertainty_score":0.729762,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05085193230268245,"score_gpt":0.3066369108940915,"score_spread":0.255784978591409,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}